This invention relates to a PID (Proportional-Integral and Differential) controller for use in feedback control and more particularly to a PID controller system in which the tuning of PID control parameters can be effected automatically.
The invention is also concerned with a system for automatically setting PID control parameters which is applicable to processes in which the ratio of dead time to time constant is large, these processes being representative of, for example, the control of combustion in boilers and the control of temperature, pH neutralization and flow rate in chemical and general industry
In the past, the tuning of PID control parameters in the PID controller is effected manually by the operator who is watching variations in control variables. This raises problems that the adjustment work becomes time-consuming and tuning results are differently affected by individuality of the operators.
On the other hand, a variety of systems based on control theory have been proposed wherein a setting test signal is applied to an object to be controlled so as to set a dynamic characteristic of the controllable object and control parameters are turned to optimum values on the basis of setting results. In these proposals, however, it is expected that because of fluctuation of control variables due to the application of the setting test signal, quality is degraded or particularly in a plant of high non-linearity, abnormal states disadvantageously take place. Further, unless the setting test is performed each time the dynamic characteristic of the controllable object is changed, optimum values of control parameters can not be obtained, thus leading to troublesome handling operations
As described in "Expert Self-tuning Controller", Measurement Technology, pp 66-72, Nov., 1986, a heuristic method (expert method) is also known wherein the tuning of control parameters is effected in consideration of the shape of responses of control variables. According to this method, an actual response shape is collated with a plurality of fundamental response shapes prepared in advance and an optimum rule is selected from a plurality of adjustment rules for a matched fundamental response shape in accordance with the actual response shape or transient trend thereof, so that PID control parameters may be modified. Disadvantageously, in this method, it is expected that the number of adjustment rules is increased, resulting in an increase in memory capacity
For example, "PID Self-tuning Based on Expert Method", Measurement Technology, pp 52-59, Nov., 1986 is relevant to this type of method.
At start-up of a plant incorporating controllable objects such as processes and a PID controller for controlling the objects, it is general practice that the time response of a process variable appearing when a manipulated variable standing for an input signal to a process is changed stepwise is set in terms of a dead time characteristic and a primary time lag characteristic and PID control parameters are adjusted to optimum values on the basis of process gain K, dead time L and time constant T in these characteristics. Such a method for optimum adjustment of PID control parameters based on the step response includes a Ziegler-Nichols (ZN) method and a Chein-Hrones-Reswick (CHR) method. These methods feature simplified computations but are disadvantageous in the following points. As an example, when PID control parameters are adjusted, pursuant to the ZN method, for a controllable object having the dead time and secondary time lag characteristics, the control response changes as the command value changes in unit step, as graphically illustrated in FIG. 1A for L/T=0.14 and in FIG. 1B for L/T=1.0. Alternatively, when PID control parameters are adjusted pursuant to the CHR method, the control response changes as the command value changes in unit step, as graphically illustrated in FIG. 3A for L/T=0.14, in FIG. 3B for L/T=1 and in FIG. 3C for L/T=5. Thus, in the ZN method, the control response deviates from the stable limit at L/T=1 and in the CHR method the control response pulsates at L/T=5. Gathering from this, it is concluded that in any of the two methods excellent control can not be realized for large values of L/T.
On the other hand, as a general-purpose method for adjustment of PID control parameters' there is available a partial model matching method as described in, for example, "Design Method for Control System Based on Partial Knowledge of Controllable Object", Transactions of The Society of Instrument and Control Engineers, Vol 5, No. 4, pp 549/555, Aug., 1979.
The outline of the partial model matching method will now be described briefly. An arrangement for implementation of the partial model matching method is schematically illustrated, in block form, in FIG. 2. Referring to FIG. 2, reference numeral 1 designates a PID controller, 2 a process standing for an object to be controlled, 7 a process setter for setting a transfer function G.sub.p (S) of the process, and 11 a control parameter determiner for determining optimum values of control parameters included in a transfer function G.sub.c (S) of the PID controller.
According to the partial model matching method, the control parameters of the PID controller 1 are so determined that a closed loop transfer function W(S) covering a command value SV and a control variable PV coincides with a transfer function Gm (s, .sigma.) of a reference model representing an ideal response of the control variable PV, where S is the Laplace operator and .sigma. is a time scale coefficient. The transfer function Gp(S) of process 1 obtained from the process setter 7 is indicated by the following equation: ##EQU1## and the transfer function Gc(S) of PID controller 1 has the form of ##EQU2## where Kp, Ti and T.sub.D are control parameters respectively called proportional gain, integration time and differential time.
Accordingly, the closed loop transfer function W(s) is given by ##EQU3##
The transfer function Gm(s, o) of reference model is then given by ##EQU4## where .alpha..sub.2, .alpha..sub.3, .alpha..sub.4 --are constants related to response waveforms.
By making equation (3) coincident with equation (4), the transfer function Gc(s) of PID controller is reduced to ##EQU5## By dividing the denominator by the numerator in equation (5), there results ##EQU6##
Considering that equation (1) equals equation (2.2) the following formulas can be obtained: ##EQU7##
From equation (10), the positive minimum real root of o is determined, which is substituted into equation (8) to determine Ti. The thus determined positive minimum real root and Ti are substituted into equations (7) and (9) to determine Kp to T.sub.D. In accordance with this method, coincidence of the closed loop transfer function W(s) with the reference model Gm(s, .sigma.) of equation (4) prevails until the fourth order term of s in equation (4).
Due to the fact that the cubic algebraic equation shown in equation (10) is solved to determined .sigma., this method requires sophisticated computation for which microcomputer operations are unsuited.